The value of value

Why do we feel that prices are the appropriate measure for illustrating the value someone receives from a product?

Now I only have a limited understanding of welfare economics, but I am going to attempt to discuss the issue anyway 😉 . If anyone more knowledgeable would like to correct me I would be happy to hear from them.

In a micro sense this idea could be criticised insofar as one person may have a lower “willingness to pay” for a product which may stem from having a higher opportunity cost (as they have a lower wealth level then other people) rather than truly receiving less value from the consumption of the good/service. If this is the case we may feel that we should re-distribute the resource from the wealth to the poor in order to increase the level of aggregate welfare.

Now accepting this relative ranking of preferences and the given endowment in the market this could be a suboptimal situation in terms of welfare. After all, we know that the poor person values both of these goods more than the wealthy person (assuming no linkages between them) so “total satisfaction” in society will be maximized by this implicit “redistribution” resources. However, this does not make the price mechanism pointless, let me attempt to explain.

General equilibrium modeling

Now, looking at things in this “partial equilibrium” sense is not appropriate for working out aggregate welfare – after all, there may be substantial linkages between the consumption of goods and the opportunity costs faced by different agents from the consumption of goods and services. Yet, we can make assumptions such that a re-distribution of resources will give us a higher level of welfare.

The thing to remember here is any result that relies on us making specific assumptions involves normative assumption that are outside the scope of economic science (see rauparaha*). Now from a policy standpoint these assumption are essential, however from an economics standpoint these assumptions tell us that the result is not generally the case.

If we assume that the more generally a result holds the more likely it is too be true (an assumption that economists are implicitly very fond of) then a model with a smaller, and less restrictive set of assumption will be preferable (note that not putting something in your model is the same as assuming that the value is zero).

Now the point of this was that we were defending the price mechanism. As a result, we should be trying to look at prices through this lens.

The first theorem tells us that the equilibrium in the competitive market is pareto efficient. A pareto efficient equilibrium is one where we can only make one person better off by making another worse off – this is what we are doing in our above example. Furthermore, I realise that perfect competition is a strict assumption. However, it is only a sufficient, not a necessary condition for the result.

Ultimately, the existence of asymmetric information, externalities, and monopolies do cause problems with the price signal – however in that case the question we have to ask is whether the government intervention involved in fixing the signal is worth it (does the social benefit exceed the cost) – this is a separate issue from the one given above, and is also an issue where economics do suggest intervention (ergo why economists such as rauparaha and myself suggest externality taxes).

Second welfare theorem

Ok, so the first welfare theorem told us what we already knew – in a static sense, taking resources from one person and giving them to another is not a pareto improvement, we have to make someone worse off to do it. This by itself does not defend prices.

However, the second welfare theorem does. Ultimately, the second theorem states that any pareto efficient equilibrium can be supported by a set of prices and a transfer of resources (given assumptions such as diminishing marginal utility).

As a result, if we have assume some cardinal ranking for peoples satisfaction in the economy (which is a normative assumption) we can reach the most efficient equilibrium by letting the market set prices following a transfer of the initial endownment of resources.

This suggest that the best way to improvement outcomes would be to take some resources from those that receive a low value on the additional dollar of spending and give it to those who receive a higher value (this ignores investment and values on fairness etc). In this case, the set of market prices will eventually adjust such that resources are allocated efficiently, and given our value judgments they will be allocated in a way that increases social welfare.

Conclusion

Now I am not saying that we should take this as a case for constantly transferring resources – after all, we had to rely on a very specific value judgment in order to reach this outcome. It does tell us though that if we do rank a different equilibrium higher we should change the endowment of initial resources rather than messing around with the pricing system or directly regulating the market.

However, it does seem to indicate that the price mechanism is a great way for resources to be allocated!

“were pareto efficient then it would be in the process of happening now.”

No it wouldn’t if initial endowments are different.

As I said at the beginning, someone may value a product more (in the sense of the utility they gain) but their “willingness to pay” may be lower because they have a lower level of wealth than other people in society – implying that their opportunity cost from buying the product is higher (as they have less resources and so would have to sacrifice buying something that they value at an even higher rate).

An easier way to state this is that if we had two people with the same utility function (and no altruistic values) but different initial endowments (in terms of utility value), the person with the greater endowment would end up better off through free market trade – even though it would be welfare maximising to have an equilibrium where they both consume exactly the same amount (given our assumption about the individuals utility functions). Note the equilibrium would be pareto efficient – but it’s not welfare maximising given our normative judgment and the full set of potential pareto efficient equilibrium.

Fundamentally, this is one of the differences between willingness to pay and the marginal utility that someone receives. (Prices captures the impact of relative marginal utility (as the price ratio equals the marginal rate of substitution), but it doesn’t necessarily capture the absolute value between market participants.

Given different endowment structures we receive different pareto efficient equilibrium (assuming that we achieve uniqueness – which in itself is unlikely). Now as they are pareto efficient we can’t objectively rank them.

However, if we have a set of value judgments we can apply them to rank the equilibria and decide what the optimal initial endowment of resources would be – give these assumptions.

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I am not trying to defend transfers – as you can see we need to discuss why we believe someone “values” the product more in the first place. However, even if we were incredibly left-wing and wanted to redistribute to hell, we should still leave prices to the market and redistribute the initial endowment to get where we want.